Is an online payments processor sign up really tied to just the website you sign up with?

When you try to sign up to online payment processors like CCBill, Stripe, Epoch, Verotel and Paysa they want to know the URL for the website on which you want to accept payments. But what if you have several websites and webshops you want to use your account with?
Is such a sign up really tied to just the website you sign up with? Or can you sign up w/ let's say a more general ecom store or website but then use your account also for other (ecom or adult) websites you have?

When you try to sign up to online payment processors like CCBill, Stripe, Epoch, Verotel and Paysa they want to know the URL for the website on which you want to accept payments. But what if you have several websites and webshops you want to use your account with?
Is such a sign up really tied to just the website you sign up with? Or can you sign up w/ let's say a more general ecom store or website but then use your account also for other (ecom or adult) websites you have?

After signing up, you'll either enter the other websites or it won't ask you for them and you can just use the payment processor however you want.

Part of what your discount fee charges will be (with some processing companies) and whether or not they will even accept you for processing depends on the website. There are plenty of product niches where processing companies will not touch a website. Some companies will let you set up multiple websites under one processing account, but you still need to have every single website approved for processing.